论文标题
通用量子（半）组和HOPF信封
Universal quantum (semi)groups and Hopf envelopes
论文作者
论文摘要
我们证明，在$ a（c）$ = frt构造的情况下，编织矢量空间$（v，c）$承认一个弱的frobenius代数$ \ mathfrak b $（例如，编织是刚性的，nichols代数且其nichols代数是$ a的$ a（c）$ a（c）$ a（c），$ a（c）$ a（c）$ a（c）$ a（C）与弱的Frobenius代数相关的决定因素。这概括了作者在\ cite {fg}中与gastónA。garcía一起的结果，在那里证明了同样的陈述，但是我们现在知道的额外假设是不必要的。在途中，我们描述了一种通用方式，它构建了一个连接到有限维矢量空间的通用bialgebra，以及由地图家族$ \ {f_i：v^{\ otimes n_i} \ \ to v^{\ otimes m_i} \} $给出的一些代数结构。 Dubois-Violette和Launer Hopf代数以及FRT建筑的共同三角形特性在证明上起着基本作用。
We prove that, in case $A(c)$ = the FRT construction of a braided vector space $(V,c)$ admits a weakly Frobenius algebra $\mathfrak B$ (e.g. if the braiding is rigid and its Nichols algebra is finite dimensional), then the Hopf envelope of $A(c)$ is simply the localization of $A(c)$ by a single element called the quantum determinant associated to the weakly Frobenius algebra. This generalizes a result of the author together with Gastón A. García in \cite{FG}, where the same statement was proved, but with extra hypotheses that we now know were unnecessary. On the way, we describe a universal way of constructing a universal bialgebra attached to a finite dimensional vector space together with some algebraic structure given by a family of maps $\{f_i:V^{\otimes n_i}\to V^{\otimes m_i}\}$. The Dubois-Violette and Launer Hopf algebra and the co-quasi triangular property of the FRT construction play a fundamental role on the proof.
